Entropy can lead to order, paving the route to nanostructures

Computer simulations by University of Michigan researchers Pablo Damasceno, Sharon Glotzer, and Michael Engel have shown how entropy can nudge nanoparticles into organized structures. They can even predict what kinds of structures will form. Photo: Laura Rudich

Researchers trying to herd
tiny particles into useful ordered formations have found an unlikely ally:
entropy, a tendency generally described as "disorder."

Computer simulations by
University of Michigan scientists and engineers show that the property can
nudge particles to form organized structures. By analyzing the shapes of the
particles beforehand, they can even predict what kinds of structures will form.

The findings, published in Science, help lay the ground rules for
making designer materials with wild capabilities such as shape-shifting skins
to camouflage a vehicle or optimize its aerodynamics.

Physicist and chemical
engineering professor Sharon Glotzer proposes that such materials could be
designed by working backward from the desired properties to generate a
blueprint. That design can then be realized with nanoparticles—particles a
thousand times smaller than the width of a human hair that can combine in ways
that would be impossible through ordinary chemistry alone.

One of the major challenges
is persuading the nanoparticles to create the intended structures, but recent
studies by Glotzer's group and others showed that some simple particle shapes
do so spontaneously as the particles are crowded together. The team wondered if
other particle shapes could do the same.

"We studied 145
different shapes, and that gave us more data than anyone has ever had on these
types of potential crystal-formers," Glotzer SAID. "With so much
information, we could begin to see just how many structures are possible from
particle shape alone, and look for trends."

Using computer code written
by chemical engineering research investigator Michael Engel, applied physics
graduate student Pablo Damasceno ran thousands of virtual experiments,
exploring how each shape behaved under different levels of crowding. The
program could handle any polyhedral shape, such as dice with any number of
sides.

Left to their own devices,
drifting particles find the arrangements with the highest entropy. That
arrangement matches the idea that entropy is a disorder if the particles have
enough space: they disperse, pointed in random directions. But crowded tightly,
the particles began forming crystal structures like atoms do—even though they
couldn't make bonds. These ordered crystals had to be the high-entropy
arrangements, too.

Shapes can arrange themselves into crystal structures through entropy alone, new research from the University of Michigan shows. Image credit: P. Damasceno, M. Engel, S. Glotzer

Glotzer explains that this
isn't really disorder creating order—entropy needs its image updated. Instead,
she describes it as a measure of possibilities. If you could turn off gravity
and empty a bag full of dice into a jar, the floating dice would point every
which way. However, if you keep adding dice, eventually space becomes so
limited that the dice have more options to align face-to-face. The same thing
happens to the nanoparticles, which are so small that they feel entropy's
influence more strongly than gravity's.

"It's all about
options. In this case, ordered arrangements produce the most possibilities, the
most options. It's counterintuitive, to be sure," Glotzer said.

The simulation results
showed that nearly 70% of the shapes tested produced crystal-like structures
under entropy alone. But the shocker was how complicated some of these structures
were, with up to 52 particles involved in the pattern that repeated throughout
the crystal.

The particle shapes
produced three crystal types: regular crystals like salt, liquid crystals as
found in some flat-screen televisions and plastic crystals in which particles
can spin in place. By analyzing the shape of the particle and how groups of
them behave before they crystallize, Damasceno said that it is possible to
predict which type of crystal the particles would make.

"The geometry of the
particles themselves holds the secret for their assembly behavior," he
said.

Why the other 30% never
formed crystal structures, remaining as disordered glasses, is a mystery.

"These may still want
to form crystals but got stuck. What's neat is that for any particle that gets
stuck, we had other, awfully similar shapes forming crystals," Glotzer
said.

In addition to finding out
more about how to coax nanoparticles into structures, her team will also try to
discover why some shapes resist order.